descartes noted that he had many beliefs. he also noted that through the course of his life he had discovered that many of his beliefs were in error. he wanted to secure knowledge on firm foundations and so he locked himself away in his oven room with a question 'what knowledge is there in the world that is so certain that no rational man could doubt it?'

now if he had attempted to list all of his beliefs in order to assess them one at a time he would have died before completion as people have an indefinately large number of beliefs. (i believe that 2 is greater than one, i believe that 3 is greater than 1, i believe that 4 is greater than one etc etc). so in order to save a little time descartes divided knowledge up into two kinds: 1) a-priori knowledge (knowledge prior to experience or that can be worked out on the basis of reflection alone like mathematical and logical truths). 2) a-posteriori knowledge (knowledge post, or after experience or that which is based on observation like the natural sciences).

Regarding a-posteriori knowledge he says that sometimes he dreams and yet he thinks he is awake. it is thus possible that that is happening to him now. as such all the beliefs he has about where he is and what is in the world might be false. a rational man can doubt all the deliverances of science because he might well have dreamed the deliverances (this is aka 'brain in a vat' scepticism that has been popularised by 'the matrix').

Regarding a-priori knowledge he says that sometimes he makes a mistake when he does math or logic. it is possible that there is some evil genius / demon who is systematically leading him into error every time he attempts to add 2 and 2. since he can't rationally rule this out it is possible for a rational man to doubt his a-priori beliefs.

then he says that hard as the evil demon could be intent on deceiving him by leading into systematic error it seems that the evil demon must be persuading SOMETHING. so long as he was thinking HE WAS THINKING. from this comes descartes first indubitable proposition (that no man can rationally doubt)

cogito ergo sum

which is sometimes translated as:

i think, therefore, i exist.

(there is a joke about 'i drink, therefore, i exist'. this does not work for the reason that the dream argument rules out your indubitably knowing that you drink).

this is problematic for a number of reasons:

who is the I who does the thinking? (descartes was a substance dualist but this is a since discredited position)

the use of 'therefore' makes it sound like an inference. but we can rationally doubt inferences (as shown by the evil demon argument)

so sometimes it is translated

cognition = existence

roughly... roughly...

there is a thought

there is a thought

apparantly i don't have an i

but there is a thought

(from here he offers arguments for the existence of god being indubitable and from there the notion that clear and distinct ideas are true. this is sometimes called 'the cartesian circle' because he relies on clear and distinct ideas being true in order to prove god exists and he relies on the existence of god assuring that clear and distinct ideas are true)

that is one take.

another is this:

clear and distinct ideas = god

if you apprehend the equivalence before your mind
(so it is not an inference)
if you apprehend the equivalence before your mind
(the whole thing)
it is self-evident such that no rational man can doubt it

like
2+2=4
like
p=p
like
either 'goldbachs conjecture is true'
or 'goldbachs conjecture is false'
(whichever it is)
when apprehended by an infinite mind
(clear and distinct ideas = god)

indubitable...
but strangely empty